Find the Power Series representation of f(x)=ln(1-x^2)

The function f(x)=ln⁡〖(1−x^2)〗 is represented as a power series f(x)=∑_(n=0)^∞ c_n x^n
Find c_0, c_1,c_2,c_3,c_4, and the radius of convergence of the series
In this Calculus 2 problem, we derive the power series for ln(1-x) from the geometric series, then use that series to answer the question. Enjoy!

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Consider the region R delimited by the curve y = C − x2 and the x axis. use integration to find the value of C > 0 so that the volume of the solid obtained by rotating R around the x axis is 64√2/15πu.v. Note: Plane sections known to the x axis are circles. Would you help me?